**4. Convergence Criteria**

HAM was applied to compute the solution of the problems given in Equations (7)–(9), (20), and (21), as HAM contains the non-zero auxiliary parameter *i*(*i* = 1 − <sup>5</sup>), which ensures the convergence of the solution. To ge<sup>t</sup> a suitable value for the *i*, *i*− curves are displayed. To guarantee the convergence, 20th order *i*− curves have been drawn in Figures 2–6. It can easily be seen from the *i* curves that the acceptable values of *i* were 0.5 ≤ -1 ≤ 1.5, − 1.5 ≤ -2 ≤ −0.5, 0 ≤ -3 ≤ 6, for the long slider. Similarly, acceptable values for the circular slider were 0.5 ≤ -4 ≤ 1.5, − 1 ≤ -5 ≤ 4.

**Figure 2.** -1 for the strip/long slider.

**Figure 3.** -2 for the strip/long slider.

**Figure 4.** -3 for the strip/long slider.

**Figure 5.** -4 for the circular slider.

**Figure 6.** -5 for the circular slider.
